LCM of 36, 60 and 72 is equal to 360. The comprehensive work provides more insight of how to find what is the lcm of 36, 60 and 72 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 36, 60 and 72?
lcm (36 60 72) = (?)
36 => 2 x 2 x 3 x 3
60 => 2 x 2 x 3 x 5
72 => 2 x 2 x 2 x 3 x 3
= 2 x 2 x 3 x 3 x 5 x 2
= 360
lcm (36, 60 and 72) = 360
360 is the lcm of 36, 60 and 72.
where,
36 is a positive integer,
60 is a positive integer,
360 is the lcm of 36, 60 and 72,
{2, 2, 3, 3} in {2 x 2 x 3 x 3, 2 x 2 x 3 x 5, 2 x 2 x 2 x 3 x 3} are the most repeated factors of 36, 60 and 72,
{5, 2} in {2 x 2 x 3 x 3, 2 x 2 x 3 x 5, 2 x 2 x 2 x 3 x 3} are the the other remaining factors of 36, 60 and 72.
Use in Mathematics: LCM of 36, 60 and 72
The below are some of the mathematical applications where lcm of 36, 60 and 72 can be used:
The below solved example with step by step work shows how to find what is the lcm of 36, 60 and 72 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 36, 60 and 72?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 36
B = 60
C = 72
What to be found:
find the lcm of 36, 60 and 72
step 2 Find the prime factors of 36, 60 and 72:
Prime factors of 36 = 2 x 2 x 3 x 3
Prime factors of 60 = 2 x 2 x 3 x 5
Prime factors of 72 = 2 x 2 x 2 x 3 x 3
step 3 Identify the repeated and non-repeated prime factors of 36, 60 and 72:
{2, 2, 3, 3} are the most repeated factors and {5, 2} are the non-repeated factors of 36, 60 and 72.
step 4 Find the product of repeated and non-repeated prime factors of 36, 60 and 72:
= 2 x 2 x 3 x 3 x 5 x 2
= 360
lcm(20 and 30) = 360
Hence,
lcm of 36, 60 and 72 is 360
2 | 36 | 60 | 72 |
2 | 18 | 30 | 36 |
2 | 9 | 15 | 18 |
3 | 9 | 15 | 9 |
3 | 3 | 5 | 3 |
5 | 1 | 5 | 1 |
1 | 1 | 1 |